The purpose of this monograph is to present results obtained by the author in his research on spaces which are, at the same time,equipped with a topological strucutre and an order structure. Starting from the fundamental, now classical, wvork of P. Urysohn and Andr? Weil in general topology, the author introduces the concepts of a normallv ordered space, a compact ordered space, and a uniform ordered space, and generalizes the most outstanding results and aspects of the theory developed by Urysohn and Weil to these spaces.